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Your search for courses · during 26SP · tagged with MATH Algebra · returned 2 results
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MATH 352 Galois Theory 6 credits
In the nineteenth century, Évariste Galois discovered a deep connection between field theory and group theory. Now known as Galois theory, this led to the resolution of several centuries-old problems, including whether there is a version of the quadratic formula for higher-degree polynomials, and whether the circle can be squared. Today Galois theory is a fundamental concept for many mathematical fields, from topology to algebra to number theory. This course develops the theory in a modern framework, and explores several applications. Topics include field extensions, classical constructions, splitting fields, the Galois correspondence, Galois groups of polynomials, and solvability by radicals.
This course can be repeated only by students who took MATH 352 22-23
- Spring 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 342 with grade of C- or better.
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MATH 362 Representation Theory of Finite Groups 6 credits
Representation theory is the study of mathematical structures via the tools of linear algebra. The first objects to be studied in this way were finite groups at the end of the nineteenth century, motivated by the powerful framework of characters in number theory, but the field has generalized incredibly due to the prevalence of symmetry throughout mathematics, physics, and beyond. In this course the focus is on finite groups. Topics include Maschke’s theorem, complete reducibility, and Schur’s lemma; characters, orthogonality relations, and character tables; Fourier transformations and random walks. Additional topics may include Burnside’s Lemma, Frobenius reciprocity, and an exploration of representations of infinite groups.
- Spring 2026
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 342 with grade of C- or better.